Answer:
Lateral surface area = 106.4 [tex]in^{2}[/tex].
Step-by-step explanation:
Assumed that the oatmeal container has the shape of a cylinder. Its lateral surface area can be determined by:
lateral surface area = 2[tex]\pi[/tex]rh
But,
volume = [tex]\pi[/tex][tex]r^{2}[/tex]h
where: r is the radius, and h is the height.
From the question, volume = 239.4 [tex]in^{3}[/tex], and diameter = 9 inches, then;
radius = [tex]\frac{diameter}{2}[/tex] = [tex]\frac{9}{2}[/tex]
= 4.5
radius = 4.5 inches
Thus,
volume = [tex]\pi[/tex][tex]r^{2}[/tex]h
239.4 = [tex]\pi[/tex]x [tex](4.5)^{2}[/tex] x h
= 20.25[tex]\pi[/tex]h
h = [tex]\frac{239.4}{20.25\pi }[/tex]
= [tex]\frac{11.8222}{\pi }[/tex]
h = [tex]\frac{11.8222}{\pi }[/tex] inches
Therefore,
lateral surface area = 2[tex]\pi[/tex]rh
= 2[tex]\pi[/tex](4.5)([tex]\frac{11.8222}{\pi }[/tex])
= 2 x 4.5 x 11.8222
= 106.3998
Lateral surface area of the oatmeal container is 106.4 [tex]in^{2}[/tex].
